Now suppose the initial velocity of the train is 4 m/s and the hill is 4 meters tall. If the train has a mass of 30000 kg, what is the value

Question

Now suppose the initial velocity of the train is 4 m/s and the hill is 4 meters tall. If the train has a mass of 30000 kg, what is the value of the spring constant if the spring is compressed from its rest length to a maximum depth of 2.4 m by the train

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Acacia 3 years 2021-08-14T23:17:54+00:00 1 Answers 18 views 0

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  1. Doris
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    2021-08-14T23:19:47+00:00
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    Answer:

    187,500N/m

    Explanation:

    From the question, the kinectic energy of the train will be equal to the energy stored in the spring.

    Kinetic energy = 1/2 mv² and energy stored in a spring E = 1/2 ke².

    Equating both we will have;

    1/2 mv² = 1/2ke²

    mv² = ke²

    m is the mass of the train

    v is the velocity of then train

    k is the spring constant

    e is the extension caused by the spring.

    Given m = 30000kg, v = 4 m/s, e = 4 – 2.4 = 1.6m

    Substituting this values into the formula will give;

    30000*4² =  k*1.6²

    k = \frac{30,000*16}{1.6^2}\\ \\k = \frac{480,000}{2.56}\\ \\k = 187,500Nm^{-1}

    The value of the spring constant is 187,500N/m

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